A368129 A variant of A367146 with application of the distance minimization to the second of two symmetrized versions of the strip bijection between two square lattices as described in A368126.

1, 8, 12, 24, 72, 156, 168, 216, 264, 624, 1560, 1752, 1836, 2232, 4824, 12456, 13080, 16380, 17064, 35040, 92184, 92952, 123096, 128844, 244584, 639192, 651432, 855240, 945756

Offset: 1

Author

Hugo Pfoertner, Jan 03 2024

Keywords

• nonn
• more

Comments

Apparently, a(n) == 0 (mod 4) for n > 1. For cycles, whose lengths are multiples of 8, the visited points form 8 separated islands.

Larger terms are 1660752, 4293336, 4462104, 5787768, 6647916, 11050488, 28333080, 38414184, 45366204, 184427544.

Examples

			See files linked in A368130 for visualization of orbits.
		

Links

• Hugo Pfoertner, Example of one of the 8 islands in orbit with L=184427544.

Crossrefs

Cf. A307110, A367146, A367150, A368126.

A368130 is a permutation of this sequence.

A368124 is the analog for the first symmetrized version of the strip bijection.

Programs

PARI

\\ Uses definitions and functions from
\\ a367150_PARI.txt and a368126_PARI.txt
cycle(v) = {my (n=1, w=BijectionD(v, Bijectionk)); while (w!=v, n++; w=BijectionD(w, Bijectionk)); n};
a368129(rmax=235) = {my (L=List()); for (r2=0, rmax^2, for (x=0, sqrtint(r2), my (y2=r2-x^2, y); if (issquare(y2, &y), if(x>=y, my (c=cycle([x, y])); if (setsearch(L, c)==0, print([c, [x, y], sqrt(x^2+y^2)], ", "); listput(L, c); listsort(L, 1)))))); L};
a368129() \\ Terms < 1000, takes 5-10 minutes CPU time